Engineering Entrance Exam Preparation Resources

Engineering Entrance

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Q. If a 2 kg object is dropped from a height, what is its velocity just before hitting the ground (g = 10 m/s²)? (2023)

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Using v = √(2gh), for h = 10 m, v = √(2 * 10 m/s² * 10 m) = √200 = 20 m/s.

Correct Answer: B — 20 m/s

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Q. If a 2 kg object is moving with a velocity of 15 m/s, what is its kinetic energy?

A. 225 J
B. 150 J
C. 300 J
D. 450 J

Solution

Kinetic Energy = 1/2 * m * v^2 = 1/2 * 2 kg * (15 m/s)^2 = 225 J.

Correct Answer: A — 225 J

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Q. If a 2 kg object is moving with a velocity of 3 m/s, what is its kinetic energy?

A. 9 J
B. 6 J
C. 3 J
D. 12 J

Solution

Kinetic Energy = 0.5 * m * v² = 0.5 * 2 kg * (3 m/s)² = 9 J.

Correct Answer: A — 9 J

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Q. If a 5 kg object is moving with a velocity of 3 m/s, what is its momentum? (2023)

A. 5 kg·m/s
B. 10 kg·m/s
C. 15 kg·m/s
D. 20 kg·m/s

Solution

Momentum p = mv = 5 kg * 3 m/s = 15 kg·m/s.

Correct Answer: C — 15 kg·m/s

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Q. If a 5 kg object is subjected to a net force of 20 N, what is its acceleration? (2023)

A. 2 m/s²
B. 4 m/s²
C. 5 m/s²
D. 10 m/s²

Solution

Using F = ma, we find a = F/m = 20 N / 5 kg = 4 m/s².

Correct Answer: B — 4 m/s²

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Q. If a 5Ω resistor is connected to a 10V source, what is the power dissipated? (2023)

A. 2W
B. 5W
C. 10W
D. 20W

Solution

Power P = V²/R = (10V)² / 5Ω = 100 / 5 = 20W.

Correct Answer: C — 10W

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Q. If a 6Ω resistor is connected in parallel with a 3Ω resistor, what is the equivalent resistance? (2023)

A. 2Ω
B. 1.5Ω
C. 4Ω
D. 9Ω

Solution

Using the formula 1/R_eq = 1/R1 + 1/R2, we get 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.

Correct Answer: A — 2Ω

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Q. If a 9V battery is connected to a 3Ω resistor, what is the current flowing through it? (2021)

A. 1A
B. 2A
C. 3A
D. 4A

Solution

Using Ohm's law, I = V/R = 9V / 3Ω = 3A.

Correct Answer: B — 2A

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Q. If A = 2i + 3j and B = 3i + 4j, what is the angle between A and B? (2021)

A. 0 degrees
B. 45 degrees
C. 90 degrees
D. 180 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.7071, θ = 45 degrees.

Correct Answer: B — 45 degrees

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Q. If a = 3 and b = 4, what is the value of a^2 + b^2? (2019)

A. 25
B. 12
C. 7
D. 16

Solution

a^2 = 9 and b^2 = 16, so 9 + 16 = 25.

Correct Answer: A — 25

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Q. If A = 3i + 4j and B = 2i - j, what is A + B? (2021)

A. 5i + 3j
B. 5i + 5j
C. 1i + 5j
D. 1i + 3j

Solution

A + B = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.

Correct Answer: A — 5i + 3j

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Q. If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)

A. 0
B. 8
C. 12
D. 16

Solution

B × A = |i  j  k| |-1  3  0| |4  2  0| = 0, hence A · (B × A) = 0.

Correct Answer: A — 0

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Q. If A = 5i + 12j, what is the unit vector in the direction of A? (2021)

A. (5/13)i + (12/13)j
B. (12/13)i + (5/13)j
C. (5/12)i + (12/5)j
D. (12/5)i + (5/12)j

Solution

Unit vector = A / |A| = (5i + 12j) / √(5^2 + 12^2) = (5/13)i + (12/13)j.

Correct Answer: A — (5/13)i + (12/13)j

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Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)

A. -3i - 3j - 3k
B. -3i - 3j + 3k
C. 3i + 3j + 3k
D. 3i + 3j - 3k

Solution

A - B = (1 - 4)i + (2 - 5)j + (3 - 6)k = -3i - 3j - 3k.

Correct Answer: A — -3i - 3j - 3k

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Q. If a capacitor is charged to 12V and has a capacitance of 6μF, what is the stored energy? (2022)

A. 0.432 mJ
B. 0.072 mJ
C. 0.864 mJ
D. 0.216 mJ

Solution

Energy = 0.5 × C × V² = 0.5 × 6 × 10^-6 × 12² = 0.432 mJ.

Correct Answer: A — 0.432 mJ

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Q. If a car travels at a speed of 60 km/h, how far will it travel in 2 hours? (2022)

A. 120 km
B. 100 km
C. 150 km
D. 90 km

Solution

Distance = Speed × Time = 60 km/h × 2 h = 120 km.

Correct Answer: A — 120 km

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Q. If a circle has a circumference of 31.4 cm, what is its radius? (2022)

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

Circumference = 2πr; 31.4 = 2 * π * r; r = 31.4 / (2 * π) = 5 cm.

Correct Answer: A — 5 cm

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Q. If a circle has a radius of 3 cm, what is its circumference? (Use π = 3.14) (2023)

A. 6.28 cm
B. 9.42 cm
C. 12.56 cm
D. 15.70 cm

Solution

Circumference = 2πr = 2 * 3.14 * 3 = 18.84 cm.

Correct Answer: C — 12.56 cm

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Q. If a circuit has a resistance of 5 ohms and a current of 2 A, what is the voltage? (2014)

A. 10 V
B. 5 V
C. 2 V
D. 1 V

Solution

Using Ohm's Law, V = I × R = 2 A × 5 Ω = 10 V.

Correct Answer: A — 10 V

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Q. If a circuit has a total resistance of 12Ω and a current of 1.5A, what is the voltage across the circuit? (2021)

A. 18V
B. 12V
C. 15V
D. 10V

Solution

Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.

Correct Answer: A — 18V

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Q. If a circuit has a total resistance of 12Ω and a current of 4A, what is the voltage across the circuit? (2023)

A. 48V
B. 36V
C. 24V
D. 12V

Solution

Using Ohm's law, V = IR = 4A * 12Ω = 48V.

Correct Answer: A — 48V

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Q. If a circuit has a total resistance of 8Ω and a current of 4A, what is the voltage across the circuit? (2023)

A. 32V
B. 24V
C. 16V
D. 12V

Solution

Using Ohm's law, V = IR = 4A * 8Ω = 32V.

Correct Answer: A — 32V

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Q. If a die is rolled, what is the probability of getting an even number? (2022)

A. 1/2
B. 1/3
C. 1/6
D. 2/3

Solution

Even numbers on a die = 2, 4, 6. Probability = 3/6 = 1/2.

Correct Answer: A — 1/2

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Q. If a force of 20 N moves an object 5 m in the direction of the force, what is the work done?

A. 100 J
B. 50 J
C. 20 J
D. 200 J

Solution

Work = Force * Distance = 20 N * 5 m = 100 J.

Correct Answer: A — 100 J

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Q. If a person lifts a 20 kg box to a height of 2 m, what is the work done against gravity? (g = 9.8 m/s²)

A. 392 J
B. 196 J
C. 588 J
D. 784 J

Solution

Work = m * g * h = 20 kg * 9.8 m/s² * 2 m = 392 J.

Correct Answer: B — 196 J

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Q. If a rectangle has a length of 10 cm and a width of 5 cm, what is its area? (2017)

A. 50 cm²
B. 60 cm²
C. 40 cm²
D. 30 cm²

Solution

Area = length × width = 10 cm × 5 cm = 50 cm².

Correct Answer: A — 50 cm²

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Q. If a rectangle has a length of 8 cm and a width of 3 cm, what is its area? (2015)

A. 24 cm²
B. 30 cm²
C. 20 cm²
D. 18 cm²

Solution

Area = length × width = 8 × 3 = 24 cm².

Correct Answer: A — 24 cm²

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Q. If a rectangle has a length of 8 cm and a width of 3 cm, what is its perimeter? (2019)

A. 22 cm
B. 24 cm
C. 20 cm
D. 26 cm

Solution

Perimeter = 2(length + width) = 2(8 + 3) = 22 cm.

Correct Answer: A — 22 cm

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Q. If a wave has a frequency of 50 Hz and a wavelength of 2 m, what is its speed? (2018)

A. 100 m/s
B. 50 m/s
C. 25 m/s
D. 200 m/s

Solution

Wave speed = frequency × wavelength = 50 Hz × 2 m = 100 m/s.

Correct Answer: A — 100 m/s

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Q. If a wave has a frequency of 50 Hz, what is its period? (2022)

A. 0.02 s
B. 0.5 s
C. 2 s
D. 20 s

Solution

Period (T) = 1/Frequency = 1/50 Hz = 0.02 s.

Correct Answer: A — 0.02 s

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Engineering Entrance

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